United Parcel Service Inc., the world’s largest package-delivery business, sold $2 billion of bonds to pay for pension-fund contributions as dollar- denominated corporate bond sales reached $1 trillion for 2010.

UPS Chief Financial Officer Kurt Kuehn said in an Oct. 21 conference call that the company’s pension expenses may be “volatile” in 2011 as discount rates tumble to “the lowest in recent history.” U.S. corporate pension plans fell this year into their biggest financial hole ever because interest rates plummeted to 1960s levels, according to David Bianco, chief U.S. equity strategist at Bank of America Merrill Lynch.

UPS’s U.S. pensions were underfunded by $2.41 billion on Dec. 31, 2009, and by $3.49 billion a year earlier, according to its most recent annual report.

The numbers compare with overfunding of $2.49 billion in December 2007, according to the company’s 2008 annual report. UPS has pension funding commitments of about $1 billion a year through 2012. The amount declines to $509 million in 2013, it said in the 2009 report.